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Full text of "Modeling, Analysis and Simulation of VFT for Power Flow Control through Asynchronous Power Systems"

ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 

Modeling, Analysis and Simulation of VFT for Power 
Flow Control through Asynchronous Power Systems 

Farhad Ilahi Bakhsh 1 , Shirazul Islam 2 , and Mohammad Khursheed 3 

1 Department of Electrical Engineering, Aligarh Muslim University, Aligarh, India. 

Email: farhad.engg@gmail.com 

2 Department of Electrical Engineering, Teerthankar Mahavir University, Moradabad. 

Email: shiraz.zhcet@yahoo.com 

3 Department of Electrical Engineering, Integral University, Lucknow, India. 

E-mail: khursheed20@gmail.com 



Abstract — Variable Frequency Transformer (VFT) is a 
controllable bi-directional transmission device that can 
transfer power between asynchronous networks. It avoids both 
HVDC link and FACTS based power transmission control 
system. Basically, it is a rotatory transformer whose torque is 
adjusted in order to control the power flow. In this paper, a 
simulated model of VFT is used as a controllable bidirectional 
power transmission device that can control power flow through 
the connected asynchronous power systems. A simulation 
model of VFT and its control system models are developed 
with MATLAB and a series of studies on power flow through 
asynchronous power systems are carried out with the model. 
The response characteristics of power flow under various 
torque conditions are discussed. The voltage, current, torque 
and power flow plots are also obtained. 

Index Terms — Variable frequency transformer (VFT), 
MATLAB, Asynchronous power systems, Power flow. 

I. Introduction 

The world's electric power supply systems are widely 
interconnected. This is done for economic reasons, to reduce 
the cost of electricity and to improve reliability of power 
supply [1]. There are two ways of transmission 
interconnection. One is ac interconnection, just connected 
the two synchronous networks with ac transmission lines. It 
is simple and economic but increases the complexity of power 
system operation and decreases the stabilities of the power 
system under some serious faults. Another is Back-to-Back 
HVDC interconnection. The Back-to-Back HVDC is 
asynchronous interconnection, which is implemented via 
HVDC for most cases at present. It is easy for bulk power 
transfer and also flexible for system operation. But the design 
of HVDC system is quite complicated and expensive. The 
HVDC link requires a very costly converter plant at sending 
end and an inverter plant at receiving end. Alternatively 
recently, a new technology known as variable frequency 
transformer (VFT) has been developed for transmission 
interconnections [2-17]. By adding different devices with it, 
power transmission or power flow can be controlled within 
and between power system networks in a desired way [3]. 



©2011 ACEEE 
DOI:01.LJEPE02.03.23 



II. Concept and COMPONENTS Of VFT 

A variable frequency transformer (VFT) is a controllable, 
bidirectional transmission device that can transfer power 
between asynchronous networks [4]. The construction of 
VFT is similar to conventional asynchronous machines, where 
the two separate electrical networks are connected to the 
stator winding and the rotor winding, respectively. One power 
system is connected with the rotor side of the VFT and the 
another power system is connected with the stator side of 
the VFT. The electrical power is exchanged between the two 
networks by magnetic coupling through the air gap of the 
VFT and both are electrically isolated [4-6] . 

The VFT consists of following core components: a rotary 
transformer for power exchange, a drive motor to control the 
movement or speed of the rotor and to control the transfer of 
power. A drive motor is used to apply torque to the rotor of 
the rotary transformer and adjust the position of the rotor 
relative to the stator, thereby controlling the magnitude and 
direction of the power transmission through the VFT [5]. The 
world's first VFT, was manufactured by GE, installed and 
commissioned in Hydro-Quebec's Langlois substation, where 
it is used to exchange power up to 100 MW between the 
asynchronous power grids of Quebec (Canada) and New York 
(USA) [6]. 

A stable power exchange between the two asynchronous 
systems is possible by controlling the torque applied to the 
rotor, which is controlled externally by the drive motor. When 
the power systems are in synchronism, the rotor of VFT 
remains in the position in which the stator and rotor voltage 
are in phase with the associated systems. In order to transfer 
power from one system to other, the rotor of the VFT is rotated. 
If torque applied is in one direction, then power transmission 
takes place from the stator winding to the rotor winding. If 
torque is applied in the opposite direction, then power 
transmission takes place from the rotor winding to the stator 
winding. The power transmission is proportional to the 
magnitude and direction of the torque applied. When the 
two power systems are no longer in synchronism, the rotor 
of the VFT will rotate continuously and the rotational speed 
will be proportional to the difference in frequency between 
the two power systems (grids). During this operation the 
power flow is maintained. The VFT is designed to 
continuously regulate power transmission even with drifting 

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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 



frequencies on both grids. Regardless of power transmission, 
the rotor inherently orients itself to follow the phase angle 
difference imposed by the two asynchronous systems [2]. 

HI. VFT Model And Analysis 

A. VFT Model 

In the model, the VFT is a doubly-fed wound rotor 
induction machine (WRIM), the three phase windings are 
provided on both stator side and rotor side. The two power 
systems (#1 and #2) are connected through the VFT as shown 
in Fig. 1 . The power system#l is connected to the stator side 
of the VFT, energized by voltage, V s with phase angle, e s . The 
power system#2 is connected to the rotor side of the VFT, 
energized by voltage, V with phase angle, e . A drive motor is 
mechanically coupled to the rotor of WRIM. A drive motor 
and control system are used to apply torque, T D to the rotor 
of the WRIM which adjusts the position of the rotor relative 
to the stator, thereby controlling the direction and magnitude 
of the power transmission through the VFT. 




Fig. 1 The VFT model representation 

It is better to represent the VFT model by an equivalent 
VFT power transmission or power flow model, as shown in 
Fig. 2. The power flow direction shows the power transmission 
from power system#l to power system#2 through VFT. In 
fact, the direction of power flow could be from power 
system#l to power system#2 or vice-versa depending on 
the operating conditions. If torque is applied in one direction 
then power flow takes place from power system #1 to power 
system#2. If torque is applied in opposite direction then power 
flow reverses as shown in Fig. 4. Here, in the power flow 
process, only real power flow is being discussed. 

B. VFT Analysis 

i) Power Flow from Power system#l to Power system#2 
The power flow through the variable frequency transformer 
(VFT) can be approximated as follow: 

(1) 



where, 
R™ 



P MAX Sin0 n t 



■■ Power flow through VFT from stator to rotor, 
P MAX = Maximum theoretical power flow possible through 
the VFT in either direction which occurs when the net angle 
net is near 90U. The P„ AV is given by: 

* MAX ° J 

P = Vs Vr/X (2) 

MAX sr y - ; 



©2011 ACEEE 
DOI:01.LTEPE02.03.23 



where, 

Vs = Voltage magnitude on stator terminal, 

Vr = Voltage magnitude on rotor terminal and 

X = Total reactance between stator and rotor terminals. 



riH*rrKi**ai 
'I 



— > 




-> 



rar.tr Bfwtm 

'2 



v.>" 



[M-rhr 



Fig. 2 Power flow from power system #1 to power system #2 using 

VFT 



9 =9 -(6 + 6 ) 

net s * r rr 



(3) 



Also 
where, 

6 = Phase-angle of ac voltage on stator, with respect to a 
reference phasor, 

Q = Phase-angle of ac voltage on rotor, with respect to a 
reference phasor and 

Q = Phase-angle of the machine rotor with respect to 
stator. 

Thus, the power flow through the VFT is given by: 

P VFT = ((Vs Vr/Xsr) sin(6s - (6r + drs)) (4) 
The phasor diagram showing reference phasor, Vs, Vr, Q, 
Or, m and £ net is shown in Fig. 3. 




reference 



Fig. 3 The phasors of VFT 



For stable operation, the angle 3 net must have an absolute 
value significantly less than 90U. The power transmission or 
power flow will be limited to a fraction of the maximum 
theoretical level given in (2). Here, the power transmission 
equations are analyzed based on assumption that VFT is an 
ideal and lossless machine, with negligible leakage reactance 
and magnetizing current. The power balance equation requires 
that the electrical power flowing out of the rotor winding 
must flow into the combined electrical path on the stator 
winding and the mechanical path to the drive system, i.e.. 

P, = P S + P D (5) 

where, 

P = electrical power to the stator windings, 
P = electrical power out of the rotor windings and 
P D = mechanical power from the torque-control drive 
system. 

ve ACEEE 



ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 



Since the machine behaves like a transformer, mmf provided 
by the ampere-turns of stator must balance the rotor mmf: 

N*I =N*I (6) 

where, 

N = number of turns on stator winding, 

N = number of turns on rotor winding, 

I = current to the stator winding and 

I = current out of the rotor winding. 
Both the stator and rotor windings link the same magnetic 
flux but their frequency differs such that the voltage will also 
differs by the same ratio, therefore 

V=N*f* ¥a , (7) 

V r = N*f r *i// a , (8) 

and V/N r = V/N s *f/f (9) 

where, 

f = frequency of voltage on stator winding (Hz), 
f = frequency of voltage on rotor winding (Hz), and 
\|/ = air-gap flux. 

The nature of the machine is such that in steady state, the 
rotor speed is proportional to the difference in the frequency 
(electrical) on the stator and rotor windings, 

f m =fs-fr, (10) 

and co m =f m *120/N P (11) 

where, 

f = rotor mechanical speed in electrical frequency (Hz), 
N p = number of poles in the machine, and 
co = rotor mechanical speed in rpm. 
Combining the above relationships gives the power 
exchanged with the drive system as 

P D =P r -P t = V*I r -V*I 3 

= V*I r - (N*V/N*f/f r )*(N*I/NJ 

= v*i*(i -f/f) 

or, P D = P r *(l-f/f J (12) 

It shows that the electrical power flowing out of the rotor 
winding being proportional to mechanical power of the drive 
system, stator frequency and rotor frequency. Hence, if the 
stator frequency and rotor frequency are kept constant, then 
the electrical power flowing out of the rotor winding being 
only proportional to mechanical power of the drive system. 
ii) Power Flow from Power system#2 to Power system#l 

The power balance equation requires that the electrical 
power flowing out of the stator winding must flow into the 
combined electrical path on the rotor winding and the 
mechanical path to the drive system, i.e. 





Ps = P n + 


Pr 

VFT 


(13) 


V1 


7 !i,; "" i 


(^ 


3 ) ] 7 


PunirJi^iIni 

#1 


1 ^_ L 


] J) ~ 








— fc lUrehu-knl 


em #1 using 






F link 




OlilrfOI 1 


Fig. 4 Power flow from po 

©2011 ACEEE 
DOI:01.DEPE.02.03.23 


wer s 


/stem #2 to power syst 
/FT 



where, 

P = electrical power out of the stator windings, 
P = electrical power to the rotor windings and 
P D = mechanical power from the torque-control drive 
system. 

Since the machine behaves like a transformer, the ampere- 
turns must balance between stator and rotor: 

N*I=N*I (14) 

s s r r ' 

Both the stator and rotor windings link the same magnetic 
flux but their frequency differs such that the voltage will also 
differs by the same ratio, therefore 

V s = N*f*i// a , (15) 

V r = N*f r *y/ a , (16) 

and V/N r = V/N t *f/f s (17) 

where, 

f = frequency of voltage on stator winding (Hz), 
f = frequency of voltage on rotor winding (Hz), and 
\|/ = air-gap flux. 

The nature of the machine is such that in steady state, the 
rotor speed is proportional to the difference in the frequency 
(electrical) on the stator and rotor windings, 

f m =fs-fr, (18) 

and co rm =f rm *120/N p (19) 

Combining the above relationships gives the power 
exchanged with the drive system as 

P D =P -P = V*I s -V*I r 

= V*l[- (NW/N s *f/fJ*(N*I/NJ 
= V*I*(1 -f/f) 
or, P D = P*(l -f/f) ' (20) 

It shows that the electrical power flowing out of the stator 
winding being only proportional to mechanical power of the 
drive system, rotor frequency and stator frequency. Hence, if 
the rotor frequency and stator frequency are kept constant, 
then the electrical power flowing out of the stator winding 
being only proportional to mechanical power of the drive 
system. 

IV. DIGITAL SIMULATION OF VFT 

A. MATLAB Simulation Model 

For MATLAB, here VFT is represented as a wound rotor 
induction machine (WRIM). The WRIM is doubly-fed and is 
simulated with the asynchronous machine SI units in 
MATLAB Simulink [15]. The power system#l and power 
system#2 are simulated with three phase voltage sources as 
shown in Fig. 5. The three phase voltage source 1 is 
connected to the stator side of WRIM and the three phase 
voltage source 2 is connected to rotor side of WRIM. The 
drive motor is simulated with constant block which gives 
constant torque. The torque is applied to WRIM as mechanical 
torque T . To simulate various power flow functions, other 
blocks are also used. The power system#l is kept at 400V (L- 
L) and 60Hz whereas power system#2 is kept at 300V (L-L) 
and 50 Hz. Then this simulated model, as shown in Fig. 5, is 
used to solve electric power system using VFT. Under different 
torque conditions, the power flow through power system#l 



vcACEEE 



ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 



and power system#2 is simulated. The simulated results are 
shown in Table I, Table II and Fig. 6. 



■ : I. "mi. HD+ii 



j®k-'i 








E>* 




n°r>* 






r.'arl g-l P-n. ■■ r ^fnJ 1 1 



Active Power 2 










V-l Measurement 1 




PQ^tiritii.ihm^fln PQp4i^iimi. 



Hsi«n*i 



l;ltjg0 g* Pnii*' ^**iifl2 




«H 



Tftr#,?-pmi:w 



5. MATLAB Simulation Results 

i) Power Flow from Power system#l to Power system#2 

It is evident from the simulated results that under different 
external torque condition, the power flow through the power 
system#l and power system#2 is not zero. The magnitude 
and frequency of voltage are kept same for all operating 
conditions and the power flow through power sytem#l and 
power system#2 under different torque condition are shown 
in Table I. 

TABLE I: MATLAB SIMULATION RESULTS FOR VFT 



Fig. 5 MATLAB simulation model of VFT 

represents the power flow towards the power system#l . The 
power flow through power system#l and power system#2 
with the applied torque achieved is shown in Fig. 6. 



SJSTo 


T D 


Is 


P 3 


L 


P, 




(Nm) 


(A) 


rw) 


(A) 


m 


1 





6.S13 


214 


3.33S 


36.65 


2 


5 


5,401 


lose 


3. OSS 


-7S1.9 


3 


10 


4. €3 5 


2010 


2.52S 


-1564 


4 


15 


4.S27 


2967 


3.096 


-2304 


5 


20 


5.S71 


3964 


4.51S 


-3005 



oPtteitl til W:it< vjttiit ."2 




1 
I 



■sooe 

■4606 
AppKtdTor^utjNm) 



It is clear from table I that under zero torque condition the 

power flow through the VFT is zero even though there is 

power flow through power system#l and power system#2 

i.e. VFT is taking power from both the power systems. The 

negative sign represents the power flow towards the power 

system#2. 

ii)Power Flow from Power system#l to Power system#2 

When the applied torque is in opposite direction then 
power flow direction reverses as shown in Table II. 

TABLE II: MATLAB SIMULATION RESULTS FOR VFT 



s:no 


T D 


h 


P 3 


h 


P* 




(Nm) 


(A) 


[W) 


(A) 


rw) 


i 





6.S13 


214 


3.33S 


36.65 


2 


-5 


S.5S7 


-6242 


4.937 


901 


3 


-10 


10.57 


-1416 


6.S29 


1S0S 


4 


-15 


12.6S 


-2162 


S.SS2 


2763 


5 


-20 


14.91 


-2583 


11.07 


376S 



Fig. 6 The power flow with the applied torque 

Conclusions 

From the simulated results it is evident that both the 
magnitude and direction of the power flow through the 
connected power systems are controllable by the external 
torque applied to the rotor. Moreover, power flow is directly 
proportional to the applied torque. Hence VFT technology 
provides an option for achieving real power flow control 
through asynchronous power systems. The model developed 
is successfully used to demonstrate the power flow control 
through asynchronous power systems. The direction and 
the magnitude of power flow control are achieved. Thus, the 
VFT concept discussed and its advantages are verified by 
simulation results. 



It is clear from table II as the applied torque direction reverses 
the power flow direction also reverses. The negative sign 
©2011 ACEEE 
DOI:01.LTEPE02.03.23 



-k-ACE 



ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 201 1 



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©2011 ACEEE 
DOL01.DEPE.02.03.23 



-cACEEE